The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells

Vlasov Simulations of Trapping and Inhomogeneity in Raman Scattering

We study stimulated Raman scattering (SRS) in laser-fusion conditions with the Eulerian Vlasov code ELVIS. Back SRS from homogeneous plasmas occurs in sub-picosecond bursts and far exceeds linear theory. Forward SRS and re-scatter of back SRS are also observed. The plasma wave frequency downshifts from the linear dispersion curve, and the electron distribution shows flattening. This is consistent with trapping and reduces the Landau damping. There is some acoustic ($\omega\propto k$) activity and possibly electron acoustic scatter. Kinetic ions do not affect SRS for early times but suppress it later on. SRS from inhomogeneous plasmas exhibits a kinetic enhancement for long density scale lengths. More scattering results when the pump propagates to higher as opposed to lower density.Comment: 4 pages, 6 figures. Submitted to "Journal of Plasmas Physics" for the conference proceedings of the 19th International Conference on Numerical Simulation of Plasma

Dissipative polynomials

Limited precision floating point computer implementations of large polynomial arithmetic expressions are nonlinear and dissipative. They are not reversible (irreversible, lack conservation), lose information, and so are robust to perturbations (anti-fragile) and resilient to fluctuations. This gives a largely stable locally flat evolutionary neutral fitness search landscape. Thus even with a large number of test cases, both large and small changes deep within software typically have no effect and are invisible externally. Shallow mutations are easier to detect but their RMS error need not be simple

Software robustness: A survey, a theory, and prospects

If a software execution is disrupted, witnessing the execution at a later point may see evidence of the disruption or not. If not, we say the disruption failed to propagate. One name for this phenomenon is software robustness but it appears in different contexts in software engineering with different names. Contexts include testing, security, reliability, and automated code improvement or repair. Names include coincidental correctness, correctness attraction, transient error reliability. As witnessed, it is a dynamic phenomenon but any explanation with predictive power must necessarily take a static view. As a dynamic/static phenomenon it is convenient to take a statistical view of it which we do by way of information theory. We theorise that for failed disruption propagation to occur, a necessary condition is that the code region where the disruption occurs is composed with or succeeded by a subsequent code region that suffers entropy loss over all executions. The higher is the entropy loss, the higher the likelihood that disruption in the first region fails to propagate to the downstream observation point. We survey different research silos that address this phenomenon and explain how the theory might be exploited in software engineering

Measuring failed disruption propagation in genetic programming

Information theory explains the robustness of deep GP trees, with on average up to 83.3% of crossover run time disruptions failing to propagate to the root node, and so having no impact on fitness, leading to phenotypic convergence. Monte Carlo simulations of perturbations covering the whole tree demonstrate a model based on random synchronisation of the evaluation of the parent and child which cause parent and offspring evaluations to be identical. This predicts the effectiveness of fitness measurement grows slowly as O(log(n)) with number n of test cases. This geometric distribution model is tested on genetic programming symbolic regression

A randomised controlled trial of efficacy of cognitive rehabilitation in multiple sclerosis: a cognitive, behavioural, and MRI study

Aim: To explore the efficacy of home-based, computerised, cognitive rehabilitation in patients with multiple sclerosis using neuropsychological assessment and advanced structural and functional magnetic resonance imaging (fMRI). Methods: 38 patients with MS and cognitive impairment on the Brief International Cognitive Assessment for MS (BICAMS) were enrolled. Patients were randomised to undergo 45 minutes of computerised cognitive rehabilitation using RehaCom software (n = 19) three times weekly for six weeks or to a control condition (n = 19). Neuropsychological and MRI data were obtained at baseline (time 1), following the 6-week intervention (time 2), and after a further twelve weeks (time 3). Cortical activations were explored using fMRI and microstructural changes were explored using quantitative magnetisation transfer (QMT) imaging. Results: The treatment group showed a greater improvement in SDMT gain scores between baseline and time 2 compared to the control group (p = 0.005). The treatment group exhibited increased activation in the bilateral prefrontal cortex and right temporoparietal regions relative to control group at time 3 (p < 0.05FWE  corrected). No significant changes were observed on QMT. Conclusion: This study supports the hypothesis that home-based, computerised, cognitive rehabilitation may be effective in improving cognitive performance in patients with MS. Clinical trials registration is ISRCTN54901925

Kinetic Enhancement of Raman Backscatter, and Electron Acoustic Thomson Scatter

1-D Eulerian Vlasov-Maxwell simulations are presented which show kinetic enhancement of stimulated Raman backscatter (SRBS) due to electron trapping in regimes of heavy linear Landau damping. The conventional Raman Langmuir wave is transformed into a set of beam acoustic modes [L. Yin et al., Phys. Rev. E 73, 025401 (2006)]. For the first time, a low phase velocity electron acoustic wave (EAW) is seen developing from the self-consistent Raman physics. Backscatter of the pump laser off the EAW fluctuations is reported and referred to as electron acoustic Thomson scatter. This light is similar in wavelength to, although much lower in amplitude than, the reflected light between the pump and SRBS wavelengths observed in single hot spot experiments, and previously interpreted as stimulated electron acoustic scatter [D. S. Montgomery et al., Phys. Rev. Lett. 87, 155001 (2001)]. The EAW is strongest well below the phase-matched frequency for electron acoustic scatter, and therefore the EAW is not produced by it. The beating of different beam acoustic modes is proposed as the EAW excitation mechanism, and is called beam acoustic decay. Supporting evidence for this process, including bispectral analysis, is presented. The linear electrostatic modes, found by projecting the numerical distribution function onto a Gauss-Hermite basis, include beam acoustic modes (some of which are unstable even without parametric coupling to light waves) and a strongly-damped EAW similar to the observed one. This linear EAW results from non-Maxwellian features in the electron distribution, rather than nonlinearity due to electron trapping.Comment: 15 pages, 16 figures, accepted in Physics of Plasmas (2006